Weak and strong convergence theorems for maximal monotone operators in a Banach space

DOI10.1007/s11228-004-8196-4zbMath1078.47050OpenAlexW2049216522MaRDI QIDQ1771259

Fumiaki Kohsaka, Kamimura, Shoji, Takahashi, Wataru

Publication date: 7 April 2005

Published in: Set-Valued Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11228-004-8196-4

zbMATH Keywords

resolventstrong convergenceuniformly convex Banach spacemaximal monotone operatorproximal point algorithmconvex minimization problem

Mathematics Subject Classification ID

Convex programming (90C25) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Programming in abstract spaces (90C48) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

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Cites Work

• Unnamed Item
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• Ergodic convergence to a zero of the sum of monotone operators in Hilbert space
• Geometry of Banach spaces. Selected topics
• Produits infinis de resolvantes
• Une méthode itérative de résolution d'une inéquation variationnelle
• Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
• Approximating solutions of maximal monotone operators in Hilbert spaces
• Forcing strong convergence of proximal point iterations in a Hilbert space
• Characterization of the subdifferentials of convex functions
• On the maximal monotonicity of subdifferential mappings
• On the Convergence of the Proximal Point Algorithm for Convex Minimization
• Inequalities in Banach spaces with applications
• Monotone Operators and the Proximal Point Algorithm
• Iterations of paracontractions and firmaly nonexpansive operators with applications to feasibility and optimization
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• On the Maximality of Sums of Nonlinear Monotone Operators
• Weak and strong convergence of solutions to accretive operator inclusions and applications